Equation 677 Database

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Magma 3c3a4b8e4134…

magma 3c3a4b8e4134
Size
705
Isomorphism class hash
3c3a4b8e41346c77e0c1bf444ae473dcdd4211c0961800b1d0ebd443198f9cb9
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 21:54:01
Display reorder
660,49,560,584,572,597,50,598,561,585,573,48,596,562,586,574,600,52,563,587,575,601,53,564,588,576,599,51,565,589,577,603,55,566,590,578,604,56,567,591,579,602,54,568,592,580,58,606,569,593,581,59,607,570,594,582,57,605,571,595,583,687,688,686,685,240,376,401,388,414,238,412,377,402,389,239,413,378,400,390,417,243,379,404,391,415,241,380,405,392,416,242,381,403,393,420,235,382,407,394,418,236,383,408,395,419,237,384,406,396,234,423,385,410,397,232,421,386,411,398,233,422,387,409,399,703,704,701,702,555,171,141,133,158,556,159,169,139,134,554,157,170,140,135,154,558,167,137,132,155,559,168,138,130,156,557,166,136,131,149,553,162,147,124,150,551,160,145,125,148,552,161,146,126,549,152,165,143,127,550,153,163,144,128,548,151,164,142,129,671,672,670,669,23,432,24,91,251,21,252,430,25,92,22,250,431,26,93,254,19,435,27,90,255,20,433,28,88,253,18,434,29,89,249,14,427,30,97,247,12,428,31,98,248,13,429,32,99,17,245,426,33,96,15,246,424,34,94,16,244,425,35,95,679,680,678,677,107,273,443,290,264,108,262,271,444,291,106,263,272,442,289,267,110,269,446,286,265,111,270,447,287,266,109,268,445,288,259,105,279,441,281,260,103,277,439,282,261,104,278,440,280,101,258,275,437,284,102,256,276,438,285,100,257,274,436,283,692,691,690,689,38,499,478,306,493,36,494,500,479,304,37,495,501,480,305,492,41,498,481,309,490,39,496,482,307,491,40,497,483,308,484,44,505,476,312,485,42,506,477,310,486,43,507,475,311,47,487,504,472,315,45,488,502,473,313,46,489,503,474,314,699,700,698,697,75,201,180,63,187,76,188,199,178,64,77,189,200,179,65,186,74,197,183,62,184,72,198,181,60,185,73,196,182,61,193,81,207,175,69,194,82,205,176,70,195,83,206,177,71,80,192,203,174,68,78,190,204,172,66,79,191,202,173,67,663,664,662,661,323,608,633,620,646,324,644,609,634,621,322,645,610,632,622,649,326,611,636,623,647,327,612,637,624,648,325,613,635,625,652,321,614,639,626,650,319,615,640,627,651,320,616,638,628,317,655,617,642,629,318,653,618,643,630,316,654,619,641,631,682,683,684,681,211,87,540,528,515,212,516,85,541,529,213,514,86,539,530,518,210,84,537,527,656,208,657,658,659,517,209,519,538,526,513,217,520,546,534,511,218,521,547,535,512,219,522,545,536,216,509,523,542,533,214,510,524,543,531,215,508,525,544,532,695,696,693,694,293,118,464,456,7,294,8,119,465,454,292,6,120,463,455,10,296,121,460,459,11,297,122,461,457,9,295,123,462,458,5,299,116,470,451,3,300,117,471,452,4,298,115,469,453,302,0,112,466,450,303,2,113,467,448,301,1,114,468,449,667,668,665,666,226,364,340,329,353,227,354,365,341,330,228,352,366,342,328,356,229,367,343,332,357,230,368,344,333,355,231,369,345,331,359,224,370,346,335,360,225,371,347,336,358,223,372,348,334,220,362,373,349,338,221,363,374,350,339,222,361,375,351,337,675,676,673,674 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 11, B) with E = magma#fba993da3569b4910e46b63a02193464b761c68efe01dd1a285b47fabe43afe4, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 45.

last edited by qawbecrdtey at 2026-10-03 21:54:01 · history